Cognitive reflection in experimental anchored guessing games

The cognitive reflection test or CRT (Frederick, 2005) has been found to be a reliable predictor of the degree of strategic sophistication of subjects in a variety of laboratory experiments. These studies have found that subjects who score higher in the CRT make choices that are closer to Nash equilibrium (i.e., Brañas-Garza et al., 2012). In an extended level-k model with free subjective beliefs, we theoretically decompose the closeness to equilibrium for the class of anchored guessing games introduced in Ballester et al. (2023) into two effects: subjects with a smaller distance to equilibrium must possess a higher reasoning level in the level-k hierarchy or their level-k iteration process must begin from a starting point (called “seed”) that is inherently more advantageously positioned, which translates into the concept of “seed distance” (or both). Our main experimental finding is that subjects with a higher CRT score play closer to equilibrium due to the fact that they iterate more often in their reasoning process (as in Brañas-Garza et al., 2012), yet we find no clear evidence that they have a smaller seed distance. We also find evidence of a learning or adaptation process, which can be characterized by a warm-up phase (in which subjects reduce their seed distance), followed by a learning phase (in which they increase their reasoning level, at a faster rate in subjects with higher CRT) and then a saturation phase in which no further improvements are made.